On Solving Minimization Problem and Common Fixed Point Problem Over Geodesic Spaces With Curvature Bounded Above

Abstract

In this paper, we introduce a new modified proximal point algorithm for solving minimization problems and common fixed point problem in CAT\((1)\) spaces. We prove strong and \(\Delta\)-convergence theorems under some mild conditions. Further, an application on convex minimization and common fixed point problem over CAT\((\kappa)\) spaces with the bounded positive real number \(\kappa\) are presented. Our results extend and improve the corresponding recent results in the literature.